chapter 18 models of monopoly copyright ©2002 by south-western, a division of thomson learning. all...

Chapter 18

MODELS OF MONOPOLY

Copyright ©2002 by South-Western, a division of Thomson Learning. All rights reserved.

MICROECONOMIC THEORYBASIC PRINCIPLES AND EXTENSIONS

EIGHTH EDITION

WALTER NICHOLSON

Monopoly

• A monopoly is a single supplier to a market

• This firm may choose to produce at any point on the market demand curve

Barriers to Entry

• The reason a monopoly exists is that other firms find it unprofitable or impossible to enter the market

• Barriers to entry are the source of all monopoly power– there are two general types of barriers to

entry• technical barriers• legal barriers

Technical Barriers to Entry• The production of a good may exhibit

decreasing marginal and average costs over a wide range of output levels– in this situation, relatively large-scale firms

are low-cost producers• firms may find it profitable to drive others out of

the industry by cutting prices• this situation is known as natural monopoly• once the monopoly is established, entry of new

firms will be difficult

Technical Barriers to Entry

• Another technical basis of monopoly is special knowledge of a low-cost productive technique– it may be difficult to keep this knowledge

out of the hands of other firms

• Ownership of unique resources may also be a lasting basis for maintaining a monopoly

Legal Barriers to Entry

• Many pure monopolies are created as a matter of law– with a patent, the basic technology for a

product is assigned to one firm– the government may also award a firm an

exclusive franchise to serve a market

Creation of Barriers to Entry• Some barriers to entry result from actions

taken by the firm– research and development for new products

or technologies– purchase of unique resources– lobbying efforts to gain monopoly power

• The attempt by a monopolist to erect barriers to entry may involve real resource costs

Profit Maximization• To maximize profits, a monopolist will

choose to produce that output level for which marginal revenue is equal to marginal cost– marginal revenue is less than price because

the monopolist faces a downward-sloping demand curve

• the firm must lower its price on all units to be sold if it is to generate the extra demand for this unit

Profit Maximization

• Since MR = MC at the profit-maximizing output and P > MR for a monopolist, the monopolist will set a price greater than marginal cost

C

Profits can be found in the shaded rectangle

Profit Maximization

AC

MC

DMR

Quantity

Price

Q*

The monopolist will maximize profits where MR = MC

P*

The firm will charge a price of P*

The Inverse Elasticity Rule

• The gap between a firm’s price and its marginal cost is inversely related to the price elasticity of demand facing the firm

PQeP

MCP

,

1

where eQ,P is the elasticity of demand for the entire market

The Inverse Elasticity Rule

• Two general conclusions about monopoly pricing can be drawn:– a monopoly will choose to operate only in

regions where the market demand curve is elastic

• eQ,P < -1

– the firm’s “markup” over marginal cost depends inversely on the elasticity of market demand

Monopoly Profits• Monopoly profits will be positive as long

as the market price exceeds average cost

• Monopoly profits can continue into the long run because entry is not possible– some economists refer to the profits that

monopolies earn in the long run as monopoly rents

• the return to the factor that forms the basis of the monopoly

Monopoly Profits

• The size of monopoly profits in the long run will depend on the relationship between average costs and market demand for the product

Monopoly Profits

Quantity

PriceMC

AC

MRD

Quantity

PriceMC

AC

MRD

Positive profits Zero profit

P* P*=AC

C

Q* Q*

No Monopoly Supply Curve

• With a fixed market demand curve, the supply “curve” for a monopolist will only be one point– the price-output combination where MR =

MC

• If the demand curve shifts, the marginal revenue curve shifts and a new profit-maximizing output will be chosen

Monopoly with Linear Demand

• Suppose that the market for frisbees has a linear demand curve of the form

Q = 2,000 - 20P

orP = 100 - Q/20

• The total costs of the frisbee producer are given by

TC = 0.05Q2 + 10,000


• To maximize profits, the monopolist chooses the output for which MR = MC

• We need to find total revenue

TR = PQ = 100Q - Q2/20

• Therefore, marginal revenue is

MR = 100 - Q/10

while marginal cost is

MC = 0.01Q

Monopoly with Linear Demand• Thus, MR = MC where

100 - Q/10 = 0.01Q

Q* = 500

P* = 75

• At the profit-maximizing output,

TC = 0.05(500)2 + 10,000 = 22,500

AC = 22,500/500 = 45

= (P* - AC)Q = (75 - 45)500 = 15,000


• To see that the inverse elasticity rule holds, we can calculate the elasticity of demand at the monopoly’s profit-maximizing level of output

3500

7520,

Q

P

P

Qe PQ


• The inverse elasticity rule specifies that

3

11

,

PQeP

MCP

• Since P* = 75 and MC = 50, this relationship holds

Monopoly and Resource Allocation

• To evaluate the allocational effect of a monopoly, we will use a perfectly competitive, constant-cost industry as a basis of comparison– the industry’s long-run supply curve is

infinitely elastic with a price equal to both marginal and average cost


Quantity

Price

MC=AC

DMR

If this market was competitive, output would be Q* and price would be P*

Q*

P*

Under a monopoly, output would be Q** and price would rise to P**

Q**

P**

Consumer surplus would fall

Producer surplus will rise

There is a deadweightloss from monopoly


Quantity

Price

MC=AC

DMR

Q*Q**

P*

P** Consumer surplus falls by more than producer surplus rises

Welfare Losses and Elasticity

• Assume that the constant marginal (and average) costs for a monopolist are given by C and that the compensated demand curve has a constant elasticity:

Q = Pe

where e is the price elasticity of demand (e < -1)


• The competitive price in this market will be

Pc = C

and the monopoly price is given by

e

CPm 1

1


• The consumer surplus associated with any price (P0) can be computed as

00

)(P

e

PdPPdPPQCS

11

10

1

0

e

P

e

PCS

e

P

e


• Therefore, under perfect competition

1

1

e

CCS

e

c

1

11

1

ee

C

CS

e

m

and under monopoly

Welfare Losses and Elasticity• Taking the ratio of these two surplus

measures yields1

11

1

e

c

m

eCS

CS

• If e = -2, this ratio is ½– consumer surplus under monopoly is half

what it is under perfect competition

Welfare Losses and Elasticity• Monopoly profits are given by

mmmmm QC

e

CCQQP

1

1

ee

C

e

C

e

eC

ee

m

11

11

11

1

1

Welfare Losses and Elasticity• To find the transfer from consumer

surplus into monopoly profits we can divide monopoly profits by the competitive consumer surplus

e

e

c

m

e

e

ee

e

CS

111

11

1

• If e = -2, this ratio is ¼

Monopoly and Product Quality

• The market power enjoyed by a monopoly may be exercised along dimensions other than the market price of its product– type, quality, or diversity of goods

• Whether a monopoly will produce a higher-quality or lower-quality good than it would under competition depends on consumer demand and the firm’s costs


• Suppose that consumers’ willingness to pay for quality (X) is given by the inverse demand function P(Q,X) where

P/Q < 0 and P/X > 0

• If costs are given by C(Q,X), the monopoly will choose Q and X to maximize

= P(Q,X)Q - C(Q,X)

Monopoly and Product Quality• First-order conditions for a maximum are

0),(

QCQ

PQXQP

Q

0

XCX

PQ

X

– Marginal revenue equals marginal cost for output decisions

– Marginal revenue from increasing quality by 1 unit is equal to the marginal cost of making such an increase

Monopoly and Product Quality• The level of product quality that will be

opted for under competitive conditions is the one that will maximize net social welfare

*

0),(),(

QXQCdQXQPSW

• Maximizing with respect to X yields

*

00),(

Q

XX CdQXQPX

SW

Monopoly and Product Quality• The difference between the quality choice

of a competitive industry and the monopolist is:– the monopolist looks at the marginal valuation

of one more unit of quality assuming that Q is at its profit-maximizing level

– the competitve industry looks at the marginal value of quality averaged across all output levels


• Even if a monopoly and a perfectly competitive industry chose the same output level, they might opt for diffferent quality levels– each is concerned with a different margin

in its decision making

Durable Goods

• The fact that durable goods are long-lived may mean that the monopoly may face current competition from goods that it produced previously

• To the extent that used goods are competitively priced and substitutable for new goods, monopolistic behavior will be severely constrained

Price Discrimination• A monopoly engages in price discrimination

if it is able to sell otherwise identical units of output at different prices

• Whether a price discrimination strategy is feasible depends on the inability of buyers to practice arbitrage– profit-seeking middlemen will destroy any

discriminatory pricing scheme if possible• price discrimination becomes possible if resale is

costly

Perfect Price Discrimination

• If each buyer can be separately identified by the monopolist, it may be possible to charge each buyer the maximum price he would be willing to pay for the good– perfect or first-degree price discrimination

• extracts all consumer surplus• no deadweight loss

The monopolist will continue this way until the marginal buyer is no longer willing to pay the good’s marginal cost

Q1

P1

The first buyer pays P1 for Q1 units

Q2

P2 The second buyer pays P2 for Q2-Q1 units


Quantity

Price

D

Under perfect price discrimination, the monopolist charges a different price to each buyer

MC


• Recall the example of the frisbee manufacturer

• If this monopolist wishes to practice perfect price discrimination, he will want to produce the quantity for which the marginal buyer pays a price exactly equal to the marginal cost

Perfect Price Discrimination• Therefore,

P = 100 - Q/20 = MC = 0.1Q

Q* = 266

• Total revenue and total costs will be

511,5540

100)(666

0

*

0

2

Q Q

QdQQPTR

178,32000,1005.0 2 QTC

• Profit is much larger (23,333 > 15,000)

Market Separation• Perfect price discrimination requires the

monopolist to know the demand function for each potential buyer

• A less stringent requirement would be to assume that the monopoly can separate its buyers into a few identifiable markets– follow a different pricing policy in each market– this is known as third-degree price

discrimination

Market Separation• All the monopolist needs to know in this

case is the price elasticities of demand for each market– set price according to the inverse elasticity

rule

• If the marginal cost is the same in all markets,

)1

1()1

1(j

ji

i eP

eP

Market Separation• This implies that

)1

1(

)1

1(

i

j

j

i

e

e

P

P

• The profit-maximizing price will be higher in markets where demand is less elastic

Market Separation

Quantity in Market 2Quantity in Market 1

Price

0

DDMRMR

MCMC

Q2*

P2

Q1*

P1

If two markets are separate, a monopolist can maximize profits by selling its product at different prices in the two markets

The market with the less elastic demand will be charged the higher price

Third-Degree Price Discrimination

• Suppose that the demand curves in two separated markets are given by

Q1 = 24 – P1

Q2 = 24 – 2P2

• Suppose that marginal cost is constant and equal to 6

• Profit maximization requires thatMR1 = 24 – 2Q1 = 6 = MR2 = 12 – Q2


• The optimal choices areQ1 = 9

Q2 = 6

• The prices that prevail in the two markets are

P1 = 15

P2 = 9


• The allocational impact of this policy can be evaluated by calculating the deadweight losses in the two markets– the competitive output would be 18 in market 1

and 12 in market 2

DW1 = 0.5(P1-MC)(18-Q1) = 0.5(15-6)(18-9) = 40.5

DW2 = 0.5(P2-MC)(12-Q2) = 0.5(9-6)(12-6) = 9


• If this monopoly was to pursue a single-price policy, it would use the demand function

Q = Q1 + Q2 = 48 – 3P

• So marginal revenue would beMR = 16 – (2/3)P

• Profit-maximization occurs whereQ = 15

P = 11


• The deadweight loss is smaller with one price than with two:

DW = 0.5(P-MC)(30-Q) = 0.5(11-6)(15) = 37.5

Discrimination Through Price Schedules

• An alternative approach would be for the monopoly to choose a price schedule that provides incentives for buyers to separate themselves depending on how much they wish to buy– again, this is only feasible when there are

no arbitrage possibilities

Two-Part Tariff

• A linear two-part tariff occurs when buyers must pay a fixed fee for the right to consume a good and a uniform price for each unit consumed

T(Q) = A + PQ

• The monopolist’s goal is to choose A and P to maximize profits, given the demand for the product

Two-Part Tariff• Because the average price paid by any

demander isT/Q = A/Q + P

this tariff is only feasible if those who pay low average prices (those for whom Q is large) cannot resell the good to those who must pay high average prices (those for whom Q is small)

Two-Part Tariff• One feasible approach for profit

maximization would be for the firm to set P = MC and then set A so as to extract the maximum consumer surplus from a set of buyers

• This might not be the most profitable approach

• In general, optimal pricing schedules will depend on a variety of contingencies

Regulation of Monopolies

• Natural monopolies such as the utility, communications, and transportation industries are highly regulated in many countries

Regulation of Monopolies• Many economists believe that it is

important for the prices of regulated monopolies to reflect the marginal cost of production

• An enforced policy of marginal cost pricing will cause a natural monopoly to operate at a loss– natural monopolies exhibit declining

average costs over a wide range of output


Quantity

Price

D

MRAC

MC

Because natural monopolies exhibit decreasing costs, MC falls below AC

P1

Q1

C1

An unregulated monopoly will maximize profit at Q1 and P1

P2

Q2

C2

If regulators force the monopoly to charge a price of P2, the firm will suffer a loss because P2 < C2


• One way out of the marginal cost pricing dilemma is the implementation of a discriminatory pricing scheme– the monopoly is allowed to charge some

buyers a high price while maintaining a low price for marginal users

• the high-price demanders in effect subsidize the losses of the low-price customers

cover the losses on the sales to low-price customers

The profits on the sales to high-price customers are enough to


Quantity

Price

D

ACMC

Suppose that the regulatory commission allows the monopoly to charge a price of P1 to some users

P1

Q1

C1

Other users are offered the lower price of P2

P2

Q2

C2


• Another approach followed in many regulatory situations is to allow the monopoly to charge a price above marginal cost that is sufficient to earn a “fair” rate of return on investment– if this rate of return is greater than that

which would occur in a competitive market, there is an incentive to use relatively more capital than would truly minimize costs


• Suppose that a regulated utility has a production function of the form

Q = f (K,L)

• The firm’s actual rate of return is defined as

K

wLLKPfs

),(


• Suppose that s is constrained by regulation to be equal to s0, then the firm’s problem is to maximize profits

= Pf (K,L) – wL – vK

subject to this constraint

• The Lagrangian for this problem is

L = Pf (K,L) – wL – vK + [wL + s0K – Pf (K,L)]


• If =0, regulation is ineffective and the monopoly behaves like any profit-maximizing firm

• If =1, the Lagrangian reduces toL = (s0 – v)K

which (assuming s0>v), will mean that the monopoly will hire infinite amounts of capital – an implausible result

Regulation of Monopolies• Therefore, 0<<1 and the first-order

conditions for a maximum are:

0)(

LL PfwwPfL

L

0)( 0

KK PfsvPfK

L

0),(0

LKPfswL

L

Regulation of Monopolies• The first condition suggests that the

monopoly will hire labor up to the point at which PfL = w

• For capital, the second condition implies that

(1 - )PfK = v - s0

or

1

)(

100 vs

vsv

PfK


• Because s0>v and <1, this means that

PfK < v

• The firm will hire more capital than it would under unregulated conditions– it will also achieve a lower marginal

productivity of capital

Dynamic Views of Monopoly

• Some economists have stressed the beneficial role that monopoly profits can play in the process of economic development– these profits provide funds that can be

invested in research and development– the possibility of attaining or maintaining a

monopoly position provides an incentive to keep one step ahead of potential competitors

Important Points to Note:

• The most profitable level of output for the monopolist is the one for which marginal revenue is equal to marginal cost– at this output, price will exceed marginal

cost– the profitability of the monopolist will depend

on the relationship between price and average cost


• Relative to perfect competition, monopoly involves a loss of consumer surplus for demanders– some of this is transferred into monopoly

profits, whereas some of the loss in consumer surplus represents a deadweight loss of overall economic welfare

– it is a sign of Pareto inefficiency


• Monopolies may opt for different levels of quality than would perfectly competitive firms

• Durable good monopolists may be constrained by markets for used goods


• A monopolist may be able to increase its profits further through price discrimination – charging different prices to different categories of buyers– the ability of the monopoly to practice price

discrimination depends on its ability to prevent arbitrage among buyers


• Governments often choose to regulate natural monopolies (firms with diminishing average costs over a broad range of output levels)– the type of regulatory mechanisms adopted

can alter the behavior of the regulated firm

chapter 18 models of monopoly copyright ©2002 by south-western, a division of thomson learning. all...

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